Evaluate the following $\int\frac{(\sin x+\cos x)}{\sqrt {1+\sin 2x}}dx$

Question

$\begin{array}{1 1}(A)\;x+c \\ (B)\;\frac{x^2}{2}+c \\ (C)\;-x+c \\ (D)\;-\frac{x^2}{2}+c \end{array} $